Geometric group theory, dynamics, ring theory, and logic in interaction

In this completely self-contained talk, I'll discuss various versions of the Garden of Eden theorem, the Gottschalk surjunctivity conjecture, and Kaplansky's conjecture on stable finiteness of group rings. This will include a quick review of the notions of amenability and soficity for groups, of the theory of cellular automata, and entropies of dynamical systems.